The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations

Content: 
Inside Front Cover, Page ii
Front Matter, Page iii
Copyright, Page iv
CONTRIBUTORS, Pages ix-xi
PREFACE, Page xiii
FOREWORD, Pages 3-4, I. BABUŠKA, A.K. AZIZ
CHAPTER 1 - PRELIMINARY REMARKS, Pages 5-14
CHAPTER 2 - THE FUNDAMENTAL NOTIONS, Pages 15-45
CHAPTER 3 - PROPERTIES OF SOLUTIONS OF ELLIPTIC BOUNDARY VALUE PROBLEMS, Pages 47-81
CHAPTER 4 - THEORY OF APPROXIMATION, Pages 83-110
CHAPTER 5 - VARIATIONAL PRINCIPLES, Pages 111-184
CHAPTER 6 - RATE OF CONVERGENCE OF THE FINITE ELEMENT METHOD, Pages 185-241
CHAPTER 7 - ONE PARAMETER FAMILIES OF VARIATIONAL PRINCIPLES, Pages 243-263
CHAPTER 8 - FINITE ELEMENT METHOD FOR NON-SMOOTH DOMAINS AND COEFFICIENTS, Pages 265-283
CHAPTER 9 - THE PROBLEMS OF PERTURBATIONS IN THE FINITE ELEMENT METHOD, Pages 285-301
CHAPTER 10 - THE EIGENVALUE PROBLEM, Pages 303-343
CHAPTER 11 - THE FINITE ELEMENT METHOD FOR TIME DEPENDENT PROBLEMS, Pages 345-359
PIECEWISE ANALYTIC INTERPOLATION AND APPROXIMATION IN TRIANGULATED POLYGONS, Pages 363-385, Garrett Birkhoff
APPROXIMATION OF STEKLOV EIGENVALUES OF NON-SELFADJOINT SECOND ORDER ELLIPTIC OPERATORS, Pages 387-408, J.H. Bramble, J.E. Osborn
THE COMBINED EFFECT OF CURVED BOUNDARIES AND NUMERICAL INTEGRATION IN ISOPARAMETRIC FINITE ELEMENT METHODS, Pages 409-474, P.G. Ciarlet, P.-A. Raviart
A SUPERCONVERGENCE RESULT FOR THE APPROXIMATE SOLUTION OF THE HEAT EQUATION BY A COLLOCATION METHOD, Pages 475-490, Jim Douglas Jr.
SOME L2 ERROR ESTIMATES FOR PARABOLIC GALERKIN METHODS, Pages 491-504, Todd Dupont
COMPUTATIONAL ASPECTS OF THE FINITE ELEMENT METHOD, Pages 505-524, S.C. Eisenstat, M.H. Schultz
EFFECTS OF QUADRATURE ERRORS IN FINITE ELEMENT APPROXIMATION OF STEADY STATE, EIGENVALUE AND PARABOLIC PROBLEMS, Pages 525-556, George J. Fix
EXPERIENCE WITH THE PATCH TEST FOR CONVERGENCE OF FINITE ELEMENTS, Pages 557-587, Bruce M. Irons, Abdur Razzaque
HIGHER ORDER SINGULARITIES FOR INTERFACE PROBLEMS, Pages 589-602, R.B. Kellogg
ON DIRICHLET PROBLEMS USING SUBSPACES WITH NEARLY ZERO BOUNDARY CONDITIONS, Pages 603-627, J. Nitsche
GENERALIZED CONJUGATE FUNCTIONS FOR MIXED FINITE ELEMENT APPROXIMATIONS OF BOUNDARY VALUE PROBLEMS, Pages 629-669, J.T. Oden
FINITE ELEMENT FORMULATION BY VARIATIONAL PRINCIPLES WITH RELAXED CONTINUITY REQUIREMENTS, Pages 671-687, Theodore H.H. Pian
VARIATIONAL CRIMES IN THE FINITE ELEMENT METHOD, Pages 689-710, Gilbert Strang
SPLINE APPROXIMATION AND DIFFERENCE SCHEMES FOR THE HEAT EQUATION, Pages 711-746, Vidar Thomée
THE EXTENSION AND APPLICATION OF SARD KERNEL THEOREMS TO COMPUTE FINITE ELEMENT ERROR BOUNDS, Pages 749-755, R.E. Barnhill, J.A. Gregory, J.R. Whiteman
TWO TYPES OF PIECEWISE QUADRATIC SPACES AND THEIR ORDER OF ACCURACY FOR POISSON'S EQUATION, Pages 757-761, Alan E. Berger
A METHOD OF GALERKIN TYPE ACHIEVING OPTIMUM L2 ACCURACY FOR FIRST ORDER HYPERBOLICS AND EQUATIONS OF SCHRÖDINGER TYPE, Pages 763-765, J.E. Dendy Jr.
RICHARDSON EXTRAPOLATION FOR PARABOLIC GALERKIN METHODS, Pages 767-768, G. Fairweather, J.P. Johnson
GEOMETRIC ASPECTS OF THE FINITE ELEMENT METHOD, Pages 769-783, William J. Gordon, Charles A. Hall
THE USE OF INTERPOLATORY POLYNOMIALS FOR A FINITE ELEMENT SOLUTION OF THE MULTIGROUP DIFFUSION EQUATION, Pages 785-789, H.G. Kaper, G.K. Leaf, A.J. Lindeman
A “LOCAL” BASIS OF GENERALIZED SPLINES OVER RIGHT TRIANGLES DETERMINED FROM A NONUNIFORM PARTITIONING OF THE PLANE, Page 791, Lois Mansfield
LEAST SQUARE POLYNOMIAL SPLINE APPROXIMATION, Pages 793-796, Paul D. Patent
SUBSPACES WITH ACCURATELY INTERPOLATED BOUNDARY CONDITIONS, Page 797, Ridgway Scott